How do you calculate how much weight a boat can comfortably carry? And is this directly related to displacement?

I would like to build a small outrigger (ideally with a length to beam ratio of 8:1 or more - something easy to paddle) for my kids (to carry one child of up to 40kg). A beam of about 30cm would be suitable for them and I'm guessing the height of the hull would be between 30 and 40cm. So I'd like to know how to calculate what length would cater for this.

Actually, what you need to figure out isn't displacement, but pounds per inch of immersion. All boats will have a specific rate of "sink" as weight is applied. How much "sink" is hull form (shape) and volume specific. After a fair amount of weight is added to any particular hull, it then starts to dramatically lose stability and you're in trouble.

It would be helpful if we knew what design your were working with, as it's likely the information you need, is available from the designer or manufacture. If you're attempting to design something, with as basic a question, I'd suggest you have some studying to perform, before you should risk your children on it. I'm not suggesting you would, but calculating volume is a fundamental task in design work and if this is beyond your grasp currently, then you have a way to go yet. It's not especially hard, but does require some understanding.

I've been studying yacht design books and online for the past year and have a 'fair' grasp of things - but I'm still a bit cloudy with displacement - as I've read several articles that refer to this as the load carrying capacity which I beleive not strictly true. My understanding is that displacement is how much the hull displaces on its own.

I beleive it's possible to work out all the stats of the desired hull from the spec I've noted eg: expected load to carry, width, height (draft + freeboard) and min length to weight ratio (prismatic coefficient?).

I've looked at many other plans for outriggers, kayaks and canoes so I have an idea about which shape.

I've been using FreeShip which makes it fairly quick to define a shape and to calculate hydrostatics. So really I guess I'd like to know - what's the ratio between displacement and how much the hull can carry?

There isn't any "typical" ratio, the actual figure would be application specific.

You could establish a data base for other craft of similar shape, size and configuration and arrange for a very general guide, which could serve as a starting point.

I'm not really sure what you're looking for.

You know basically what shape you want and how much you'd like it to carry. You can calculate the sinkage rate and then you have to ask yourself is this desirable or do you want more or less volume.

Prismatic Coefficient (Cp) is a number that suggests the fullness of the ends of a boat. Determining the proper Cp revolves around the desired or expected speed and it's S/L (speed/length ratio). It's usually a good idea to error on the high side for a Cp, then have too low of one, from a performance point of view.

If I were doing this I would use ABYC's standard for capacity of canoes. You start by determining maximum weight capacity This is essentially a canoe body

a. Canoes - Maximum stated capacity shall be less than or equal to that load which yields seven (7) inches (17.8 Cm)
(17.8 cm) of freeboard as shown on Figure 1;

I can't put the illustration here but what it amounts to is; determine the displacement with seven inches of freeboard left. This can be done by calculating the immersed volume and multiplying by 62.4 lbs/cu ft or simply adding weight until you have 7 inches left. The amount of weight added is the maximum weight capacity. The persons capacity can't exceed the maximum weight capacity. If you have an engine and battery subtract their weight from maximum weight capacity. Then divide the maximum weight capactiy by 165 lbs (74.8 kg)

Tim,
I consider myself a good engineer, but at best an enthusiastic amateur when it comes to boat design and building. To me "displacement" only means amount of water displaced, weight in other words. Displacement obviously varies with the load, so you have to specify if you mean empty hull displacement, maximum load displacement etc. Even if there is some sort of consensus on the meaning of "displacement" without qualifiers it was obviously lost on me.

A maximum beam of 0.3m and a length of 8*0.3 m = 2.4 m will give you a surface area less than 0.72 sqm (rectangle). A more reasonable canoe shape would probably give you 0.5 sqm or so. Assume a total weight for boat + kid of 100 kg and you find that the draft will be 20 cm.

This is a very simplistic way to calculate and assumes a flat bottom, but you get a rough estimate of the draft. I would choose to make the canoe larger e.g. 0.4 * 3 m to reduce draft, but once again I'm only an amateur. Why not look at a similar design for adults and scale it for less load to get an estimate on suitable freeboard for your design? The outriger should take care of stability problems.

The most simple way to determine the max safe load your boat can carry is to measure the volume of the immersed portion of the hull, in cubic feet, at the designed max waterline. Multiply that volume by 63 for fresh water or 64 for seawater and deduct the deadweight of the boat. The result will give you the max safe load you can carry, in Lbs.

How do you calculate how much weight a boat can comfortably carry? And is this directly related to displacement?

I would like to build a small outrigger (ideally with a length to beam ratio of 8:1 or more - something easy to paddle) for my kids (to carry one child of up to 40kg). A beam of about 30cm would be suitable for them and I'm guessing the height of the hull would be between 30 and 40cm. So I'd like to know how to calculate what length would cater for this.

Thanks very much
Tim

A nice slender form will move easily. I prefer two outriggers to one because you can set them up to have no load but still prevent capsize. A single outrigger relies on the load you place on it initially and if you want stability to avoid a flip it will carry quite a load so adds a lot of drag.

Remember your kids are growing. 40kg may be light on for a couple of years down the track.

Working with decimetres makes it easy. Lets say 3m long 0.3m wide and 0.1m draft. The displacement will be:
D = 30 x 3 x 1 x 0.6 = 54kg
(The 0.6 is referred to prismatic coefficient and will be around this number for an efficient slender hull based on rectangular cross section.)

This would be the bare minimum as the boat itself will weigh around 15kg. You need reserve buoyancy so sides need to be about 0.2m high.

I would make some allowance for growth. Maybe go to 3.6m long, 0.35m wide and design draft remains at 0.1m. You can do the sum.